Variable Capacitance Transducers The Capacitance of a two plate capacitor is given by A – Overlapping Area x – Gap width k – Dielectric constant Permitivity of vacuum Relative permitivity A change in any one of these parameters may be used for sensing Examples - Transverse displacement, rotation, and fluid level A capacitance bridge can be used to measure the change in the capacitance Other methods include measuring a change in charge Charge – charge amplifier Voltage – high impedance device in parallel Current – low impedance device in series Or inductance capacitance oscillator circuit

DC Output v o Capacitance Bridge Rotating Plate A Fixed Plate Rotation Capacitive Rotation Sensor One plate rotates and the other is stationary Common area is proportional to the angle θ The relationship is linear and K is the sensor constant Sensitivity is

Moving Plate (e.g., Diaphragm) Position x vovo Fixed Plate Capacitive Displacement Sensor One plate is attached to the moving object and the other is kept stationary Capacitance is and sensitivity is This relationship is nonlinear but can be linearized by using an op amp circuit Output v o Supply Voltage v ref + − C ref C = K/x + − A + − Op amp Capacitance Bridge

k vovo Fixed Plate Level h Liquid Displacement Measurement by changing Dielectric Displacement can be measured by attaching the moving object to a solid dielectric element placed in between the plates Liquid level as shown below can be measured as the dielectric medium between the plates changes with the liquid level Capacitance Bridge

Output v o Supply Voltage v ref + − R + − i Displacement Measurement From magnitude From phase

Supply Voltage v ref + − i Current Sensor + − Capacitive Angular Velocity Sensor

Capacitive Sensor Applications Mechanical loading effects are negligible Variations in dielectric properties due to humidity, temperature, pressure, and impurities can cause errors Capacitance bridge can compensate for these effects Sensitivity – 1pF per mm

 + AC Excitation v ref Compensator Z 1 Sensor Z 2 Bridge Completion Z3Z3 Z4Z4 Bridge Output v o v Capacitance Bridge Circuit For a balanced circuit Bridge output due to sensor change

Charge Source q Equivalent Capacitance C Piezoelectric Sensors Substances such as BaTiO 3 (barium titanate),SiO 2 (quartz in crystalline), and lead zirconate titanate can generate an electric charge when subjected to stress (strain) Applications include Pressure and strain measuring devices Touch screens Accelerometers Torque/Force sensors Piezoelectric materials deform when a voltage is applied. Applications include Piezoelectric valves Microactuators and MEMS

Output impedance of a piezoelectric sensor is very high It varies with the frequency ~MΩ at 100Hz Sensitivity Charge sensitivity For a surface area A (pressure applied – stress) Voltage sensitivity – change in voltage due to unit increment in pressure per unit thickness (d is the thickness) k is the dielectric constant of the crystal capacitor

MaterialCharge Sensitivity S q (pC/N) Voltage Sensitivity S v (mV.m/N) Lead Zirconate Titanate (PZT) Barium Titanate Quartz Rochelle Salt Piezoelectric Material Sensitivities

Piezoelectric Accelerometer Output v o Direction of Sensitivity (Input) Spring Inertia Mass Piezoelectric Element Electrodes Inertia force caused by the acceleration produces a voltage Light weight, high frequency response (1MHz) High output impedance – small voltages ~1mV High spring stiffness – natural frequency or resonant frequency is high (20kHz) Useful frequency range – 5kHz

Accelerometer Signal (dB) Frequency (Hz) 5,000 20,000 Useful Range 1 Resonance Frequency response curve of a piezoelectric accelerometer Typical accelerometer sensitivities – 10 pC/g (pico Coulomb per gravity) or 5mV/g Sensitivity depends on the piezoelectric properties and the way the inertia force is applied Large mass would result in a large force and a large output signal but Load the measurand Lower the resonant frequency

Charge Amplifier Output v o CfCf vo/K vo/K + − A + − Charge Amplifier RfRf CcCc C Piezoelectric Sensor Cable q K Impedance matching Reduce speed of charge leakage